The coefficient of kinetic friction for a 22 kg bobsled on a track is 0.15. What force is required to push it down a 6.0° incline and achieve a speed of 64 km/h at the end of 75 m?
First calculate the required acceleration, a, with suitable units of m/s^2.
Vfinal = 64 km/h = 17.78 m/s
Vfinal = sqrt(2 a X)
a = (Vfinal)^2/(2X) = 2.11 m/s^2
Then use Newton's second law, along the direction of motion. If the pushing force is F, the net force in the direction of motion is
Fnet = F + M*g sin6 -M*g*cos6*0.15
= M a
Use that equation to solve for F.
You could also use a conservation of energy method. (Work applied) = F*X
= PE loss + KE gain + (work against friction)
To find the force required to push the bobsled down the incline, we can start by calculating the gravitational force acting on the bobsled.
Step 1: Calculate the gravitational force:
The force due to gravity can be calculated using the formula:
Force_gravity = mass * acceleration due to gravity
Here, the mass of the bobsled is 22 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
So, Force_gravity = 22 kg * 9.8 m/s^2 = 215.6 N.
Step 2: Calculate the component of the force acting down the incline:
The force acting down the incline can be found by taking into account the angle of the incline. We can calculate the component of the gravitational force acting down the incline using the formula:
Force_down_incline = Force_gravity * sin(incline angle)
Here, the incline angle is 6.0°, so we have:
Force_down_incline = 215.6 N * sin(6.0°) = 22.56 N.
Step 3: Calculate the net force required:
The net force required will be the sum of the force down the incline and the force of kinetic friction. The force of kinetic friction can be calculated using the formula:
Force_friction = coefficient of kinetic friction * Force_normal
The force normal can be found using the formula:
Force_normal = mass * acceleration due to gravity * cos(incline angle)
Substituting the values, we have:
Force_normal = 22 kg * 9.8 m/s^2 * cos(6.0°) = 215.225 N (approximately)
Now, substituting the value of coefficient of kinetic friction (0.15), we can calculate the force of kinetic friction:
Force_friction = 0.15 * 215.225 N = 32.2838 N (approximately)
So, the net force required is:
Net_force = Force_down_incline + Force_friction
Net_force = 22.56 N + 32.2838 N = 54.8438 N (approximately).
Therefore, the force required to push the bobsled down the incline and achieve a speed of 64 km/h at the end of 75 m is approximately 54.8438 N.
To find the force required to push the bobsled down the incline, we need to consider the forces acting on the bobsled.
1. Gravitational force (weight): The weight of the bobsled can be calculated using the formula: weight = mass × gravity. So, weight = 22 kg × 9.8 m/s².
2. Normal force: The normal force exerted by the incline on the bobsled is equal in magnitude and opposite in direction to the vertical component of the weight.
3. Force of friction: The force of kinetic friction can be calculated using the formula: force of friction = coefficient of friction × normal force.
4. Applied force: This is the force we need to calculate, which is required to overcome the force of friction and accelerate the bobsled.
First, let's find the weight of the bobsled:
weight = 22 kg × 9.8 m/s² = 215.6 N
Next, let's find the normal force:
The vertical component of the weight can be calculated using the formula: weight × cos(θ), where θ is the angle of the incline.
vertical component of weight = 215.6 N × cos(6.0°)
Now, let's find the force of friction:
force of friction = coefficient of friction × normal force = 0.15 × (vertical component of weight)
Finally, to find the applied force, we need to consider the net force acting on the bobsled. It can be calculated using the formula: net force = mass × acceleration.
Since the bobsled is traveling at a constant speed of 64 km/h, the net force is zero. So, the applied force must be equal in magnitude and opposite in direction to the force of friction.
Hence, the force required to push the bobsled down the incline is equal to the force of friction, which is calculated as described above.